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There's a way to ball park it. Assume that your unit is maintaining an indoor/outdoor temperature difference of 10°. You clock the run times and find that the unit is running about 20 minutes out of the hour, or 33.33% of the time. Assuming that the heat load is proportional to the indoor/outdoor temperture difference, the unit would theoretically be able to maintain an indoor/outdoor difference of

10/(33.33/100) = 30°

if it were to run nonstop.

In reality the capacity of the system drops off as the ambient temperature increases, however the load isn't strictly propotional to the temperature difference either. The heat load does not increase at as great a rate as the temperature difference, so these two factors tend to cancel each other out to some extent.

This will be nowhere near exact, but if you find that your system is grossly oversized using this method, then it probably is grossly oversized in reality.

I remember that thread. A lot of good points raised. It would probably be more accurate to clock the runtimes on the hottest days. The percent runtime method would, for some not so obvious reasons, be more accurate at higher indoor/outdoor temp differences. I probably wouldn't try it with a temp difference below 15°.

Is it more likely that a manual J is incorrect, or a rule of thumb used to size your current system?

We are assuming that the Manual J was done correctly. I have seen some really screwed up design parameters that have produced totally whacky load calculations.

So long as the calculation was done correctly, then go with that. If you aren't sure about the load calc, call another company and ask them to do one for you so you can compare results. Be prepared to pay for their time if you want to see the load calculation report.